Question

A tank had 6 liters of water. The tank had a small hole in its base through which water leaked out at a constant rate. The tank was empty after 4 minutes. If y represents the number of liters of water in the tank and x represents the time in minutes, which graph best represents this situation?

Answer 1

The graph is attached.

Explanation:

We will write an equation in slope-intercept form to represent this situation. Slope-intercept form is

y = mx+b, where m is the slope and b is the y-intercept.

We know that the y-intercept, the initial value, is 6. This gives us

y = mx+6.

We do not know the rate of change, or slope, of this situation. We do, however, know that after 4 minutes there is 0 water left in the tank. Substituting 0 in for y and 4 in for x, we have

0 = m(4)+6

0 = 4m + 6

Subtract 6 from each side:

0-6 = 4m+6-6

-6 = 4m

Divide both sides by 4:

-6/4 = 4m/4

-1.5 = m

This gives us

y = -1.5x + 6. This can also be written as

y = -3/2x + 6.

To graph this, we begin with the y-intercept, 6. We go up to 6 on the y-axis and plot a point.

The slope tells us where to find the next point. Slope is rise/run; our slope is -3/2, so from our y-intercept, we go down 3 and right 2 to make our next point. Then we draw a line between the points.

Answer 2

Based on the given problem above, if we analyze it, we are going to look for the graph which with coordinates (0,6) which represents starting out with 6 gallons, and ending at (4,0). So, the graph that best represents this situation would be the first graph on the top left. Hope this answers your question. Have a great day!